<b>Analysis of students' learning difficulties in solving linear programming problems based on Polya's problem-solving stages</b>
Suwarni La Usa, Sardin Sardin
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Published: Oct 23, 2026
DOI: 10.56855/ijmme.v4i3.2383
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Purpose – This study aims to identify university students' learning difficulties in solving linear programming problems, based on Polya's problem-solving stages, and to propose appropriate instructional strategies to address them. Methodology – A descriptive qualitative approach was employed, involving 30 purposively selected fourth-semester students from the Mathematics Education Study Program at Universitas Dayanu Ikhsanuddin. Participants who completed the Linear Programming course were classified into high- (5), moderate- (19), and low-ability (6) groups based on their cumulative grade point average (GPA). Data were collected through problem-solving tests and semi-structured interviews and analysed using Polya's four stages of problem solving. Findings – Analysis of students' written responses and interview data revealed distinct patterns of learning difficulties across Polya's problem-solving stages. High-ability students experienced the greatest difficulty in the looking back stage (32.80%), moderate-ability students in the carrying out the plan stage (36.84%), and low-ability students in understanding the problem (30.67%), which hindered their ability to devise a plan (32.67%). These findings demonstrate that learning difficulties vary according to problem-solving ability and occur at different stages of Polya's framework. Hybrid learning supported by interactive digital modules is recommended to strengthen conceptual understanding, mathematical modeling, and reflective problem solving. Novelty – This study provides a stage-based analysis of students' learning difficulties in linear programming across different ability levels and proposes hybrid learning assisted by digital modules as an instructional solution. Significance – The findings offer practical guidance for mathematics educators in designing learning strategies to improve students' problem-solving ability in linear programming.
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